Projectile Motion Review (DOC)

Projectile Motion Review
Answer the questions as best you can. Use the formulas below to aid you in your calculations.
I strongly urge you to draw diagrams.
D=v1t + ½ at2 g = 9.8 m/s2
1. A projectile is launched horizontally with an initial velocity of 8m/s, from a height of 10m above the
ground. Determine the following:
a. How long will the projectile be in the air?
b. How far from the base of the building will the projectile land?
2. The end of a ramp is placed at the edge of a table 1.1 m above the floor. A marble rolls off the ramp
horizontally and strikes the floor a horizontal distance of 1.32 m from the edge of the table.
a. How long is the marble in the air before it strikes the floor?
b. What is the initial horizontal velocity of the marble as it leaves the ramp?
3. A water balloon is fired from ground level such that it has an initial vertical speed of 20 m/s and initial
horizontal speed of 30 m/s. How far from the point of firing does the balloon land? (Let g = 10 m/s2.)
A) 40m B) 60m C) 80m D) 120m E) 180m
4. The launch velocity of a projectile is 27 m/s at 53 above the horizontal. Draw a diagram of the
component velocities and answer the following questions.
a) What is the vertical component of it’s velocity at launch?
b) What is the horizontal component of it’s velocity?
c) Neglecting air resistance, which of these components remains constant throughout the flight path?
5. A pool ball leaves a 1.10-meter high table with an initial horizontal velocity of 3.1 m/s. Predict the
time required for the pool ball to fall to the ground and the horizontal distance between the table's edge
and the ball's landing location.
6. A soccer ball is kicked horizontally off a 25.0-meter high hill and lands a distance of 28.0 meters from
the edge of the hill. Determine the initial horizontal velocity of the soccer ball.
7. A long jumper leaves the ground with an initial velocity of 13 m/s at an angle of 34-degrees above the
horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-
jumper.
8. A football is kicked with an initial velocity of 27 m/s at an angle of 35-degrees with the horizontal.
Determine the time of flight, the horizontal distance, and the peak height of the football.
9. A plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling
horizontally at 35.0 m/s at 270 m above the ground. Find:
a. where the package strikes the ground relative to the spot it was dropped
b. the velocity of the package just before it hits the ground.
10. Delbert the stunt-emu is launched from the ground into the air by a rather powerful cannon. After 1.97
seconds he is observed to reach his maximum height of 19m. If he lands 25 meters from where he
started, what are his starting component velocities?
For the following 3 diagrams, solve for the missing value(s)
11.
12.
13.
14. A bomber is approaching its target in straight and level flight. The altitude of the bomber is such that a
bomb will take two minutes to fall. The bombardier should release the bombs
a. at the instant that the plane is passing over the target.
b. one minute before the plane passes over the target.
c. two minutes before the plane passes over the target.
d. three minutes before the plane passes over the target.
e. four minutes before the plane passes over the target.
15. A .22 caliber rifle bullet has a muzzle velocity of 322m/s. If the rifle is held perfectly level when it is
fired, how far will the bullet travel if the barrel is 1.5 m above the ground?
16. A marble fired from a slingshot has an initial velocity of 8 m/s. If the target is 10 meters away, how
high above the target would you have to aim to be sure of hitting it?
17. A cannon shoots a shell up with an initial vertical velocity component of 500 m/s and an initial
horizontal component of 400 m/s. Neglecting air resistance and the curvature of the Earth, how far
away from the cannon will the shell hit?
a. 50,000 m. b. 20,000 m. c. 40,000 m.
18. In recently released Bollywood film, Sagar will co-star with Aishwarya Rai. They compete in a frog
jumping contest. Sagar’s frog jumps with an initial velocity of 5.0 m/s at an angle of 20.5° above the
horizontal while Ash’s initial velocity is 5.4 m/s at an angle of 25.0° above the horizontal. The
winner’s frog must have the greater range. Declare a winner and prove your results.
19. An artillery gun fires a shell. The initial velocity of the shell in the x-direction is 360. m/s and the
initial velocity in the y-direction is 210. m/s. Neglecting air resistance and assuming that the gun and the
target are at the same level, find a) how long the shell will stay in the air and b) how far down range will
the shell hit the target?
20. Hank (Henry) Aaron hits a baseball 1.10 m off the ground. The ball leaves his bat with a velocity of
40.0 m/s at 37.3° above the horizontal. To score a homerun, the ball must cross a 3.00 m high fence 104
m from the batter. Did Hank score a homer? Prove your result.
21. A stone is thrown with an initial speed of 12.5m/s at an angle of 62.9 º above the horizontal from the
top of a 30.8 m tall building. Neglecting air resistance, what is the magnitude (in m/s) of the vertical
component of the rock's velocity as it hits the ground?
22. An artillery shell is fired from a cliff 24.8 m above a valley with a velocity 264 m/s at an angle 33.4 º
above the horizontal. How many seconds after being fired does the shell reach its maximum height?
23. An artillery shell is fired from a cliff 29.1 m above a valley with a velocity 202 m/s at an angle 31.9 º
above the horizontal. How far (in km) has the shell traveled horizontally when it is at its maximum
height?
24. In many locations, old abandoned stone quarries have become filled with water once excavating has
been completed. While standing on a quarry wall, a boy tosses a piece of granite into the water below. If
he throws the ball at an angle of 40° with a velocity of 8.5 m/s, and it strikes the water 11.5 m away,
how high above the water is the wall?
25. A cannon on a level plain is aimed 50deg above the horizontal and a shell is fired with a muzzle
velocity of 360m/s toward a vertical cliff 950 m away. how far above the bottom does the shell strike
the side wall of the cliff?
26. A frog is floating down a river on a lily pad, unaware that he is heading straight for water fall 9 meters
high. If the frog lands 5 meters from the edge of the water fall, what speed was he going as he went over
the edge? You can assume he went off horizontally.
27. Still a little freaked out, the frog climbs back onto the lily pad and leaps with a speed of 3.2
m/s at an angle of 30 degrees, landing on the shore 4 cm above the surface of the water.
a. What is the frog’s maximum height during his leap?
b. How far from the lily pad does he land?
28. A daredevil is shot out of a cannon at 45.0° above horizontal with an initial speed of 25.0 m/s. A net is
positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the
net be placed in order to catch the daredevil?
29. A cannon fires a cannonball from the
edge of a 100-meter cliff. If the initial
velocity was 300 m/s and the launch
angle was 30° above the horizontal, how
far away will the cannonball land?
30. You’re trying to get the attention of your friend, who is up in her
room, so you’re tossing pebbles at the window. You consistently toss
them at 15.20 m/s at 85.0° above the horizontal, and the window is
10.00 meters above the ground. How far away should you stand from
the building so that you hit the window while the pebble is on its way
up?
31. A projectile is fired with an initial speed of 72.5 m/s at an angle of 34.5º above the horizontal on a
long flat firing range. Determine (a) the maximum height, (b) the total time in the air, (c) the total
horizontal distance covered.
32. A soccer player kicks a ball at an initial velocity of 18.0 m/s at an angle of 36.0° to the horizontal.
Find the following:
a. time of flight
b. range
c. maximum height
d. velocity components at t = 0, mid-range, and at impact.
33. For the situation of problem #32 suppose the field is covered with fog down to 3. 00 m above the
ground. What are the times for the ball’s entry into and exit out of the fog?